# American Institute of Mathematical Sciences

November  2021, 14(11): 4093-4140. doi: 10.3934/dcdss.2020419

## Global weak solutions for an newtonian fluid interacting with a Koiter type shell under natural boundary conditions

 1 Bahnhofstr. 39, 71364 Winnenden, Germany 2 Mathematisches Institut, Ernst-Zermelo-Str. 1, 79104 Freiburg, Germany

* Corresponding author: Michael Růžička

Received  January 2020 Revised  June 2020 Published  November 2021 Early access  August 2020

We consider a viscous, incompressible Newtonian fluid flowing through a thin elastic (non-cylindrical) structure. The motion of the structure is described by the equations of a linearised Koiter shell, whose motion is restricted to transverse displacements. The fluid and the structure are coupled by the continuity of velocities and an equilibrium of surface forces on the interface between fluid and structure. On a fixed in- and outflow region we prescribe natural boundary conditions. We show that weak solutions exist as long as the shell does not self-intersect.

Citation: Hannes Eberlein, Michael Růžička. Global weak solutions for an newtonian fluid interacting with a Koiter type shell under natural boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (11) : 4093-4140. doi: 10.3934/dcdss.2020419
##### References:

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##### References:
Reference domain $\Omega$ with in- and outflow region $\Gamma$ and moving boundary $M$
Notations for admissible in- and outflow domains and moving domains
Extension of the fluid domain
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